The invention relates to data smoothing.
Data smoothing techniques are used to elicit trends from noisy or inconsistent data. The data may comprise any sort of data. For example, the data may be a series of data points taken over time, such as spectroanalysis data from a semiconductor etching system, output test data from a semiconductor testing system, financial data relating to prices or exchange rates that vary with time, and the like. The data may comprise any stream or array of data that varies, but includes a general trend or pattern.
A wide variety of data smoothing techniques have been devised to assist in identifying trends and patterns that may exist in the data. For example, data smoothing techniques include random, random walk, moving average, simple exponential smoothing, linear exponential smoothing, seasonal exponential smoothing, and exponential weighted moving average smoothing. All of these various types of data smoothing techniques may assist in smoothing the data, but include various tradeoffs between effectively smoothing the data and maintaining an accurate reflection of the information in the data.
For example, exponential smoothing techniques are configured to eliminate extreme variations in the data to remove noise. The effect of exponential smoothing is to remove significant variations in the signal, but still track to the overall changes in the data. If the coefficient is too low, however, the exponentially smoothed data does not match effectively the raw data in the event of a relatively sudden change in the raw data. On the other hand, if the coefficient is too high, the smoothing function loses value as more noise is returned to the original data. In many other data smoothing systems, a tradeoff occurs when optimizing for sensitivity without disrupting the smoothing.
A method and apparatus for smoothing data according to various aspects of the present invention comprises adjusting data according to a first smoothing technique and selectively adjusting the data according to a second smoothing technique. In one embodiment, the method and apparatus applies a first smoothing technique to a selected datum to adjust a value of the selected datum. The method and apparatus also compares preceding adjusted data to preceding raw data to generate a comparison result. The system may apply a second smoothing technique to the selected datum to adjust the value of the selected datum according to whether the comparison result meets a first threshold. In addition, the method and apparatus may calculate a predicted value of the selected datum and apply a third smoothing technique to adjust the value of the selected datum according to whether the predicted value meets a second threshold.